Problem: If $a + b + c = 3$ and $x + y + z = 7$, what is $-7y + 5c - 7x + 5a - 7z + 5b$ ?
$= 5a + 5b + 5c - 7x - 7y - 7z$ $= (5) \cdot (a + b + c) + (-7) \cdot (x + y + z)$ $= (5) \cdot (3) + (-7) \cdot (7)$ $= 15 - 49$ $= -34$